2 problems

de Carvalho–Hall conjecture. (a) If $q\ne q_w$, then $P$ has pseudo-Anosov braid type. (b) If $P'$ is another periodic orbit with height $q'$ and the same decoration $w$, then

For a homoclinic orbit $P^w_0$ to the fixed point $0^\infty$ of the Smale horseshoe, with code $0^\infty10w0.10^\infty$ in $\Sigma_2$ for a finite decoration word $w$, let…